October 2002

Subject: computer-go: 5x5 Go is solved
Date: Sun, 20 Oct 2002 15:27:04 -0100
From: Erik van der Werf
To: COMPUTER GO MAILING LIST
Yesterday my program solved 5x5 Go starting with the first move in the
centre. As was expected it is a win for the first player with 25 points
(the whole board belongs to black).
I used an iterative deepening Alpha-beta search (PVS) with:
- Transposition tables (2-deep replacement scheme, 2 x 2^24 entries)
- Enhanced transposition cut-offs
- Symmetry lookups in the Transposition table
- 2 killer moves
- History heuristic
- Benson's algorithm for unconditional live (extended with unconditional
territory)
- Heuristic evaluation for positions that are not fixed by benson
The solution was found at 22 ply deep (23 for the empty
board).(searching 4.472.000.000 nodes in about 4 hours on a P4 2.0Ghz)
The main reason why my search was able to solve 5x5 is Benson's
algorithm which reduced the depth where a proven full-board-win is
detected by at least 6 plies (compared to by old implementation which
had to play many things out).
Only the simple (japanese) ko-rule was used, so the result is
independent of any superko-rule. This does not mean that super-ko is
irrelevant, just that from the empty 5x5 board there is a forced line
that avoids all long cycles.

December 2002

Our program now has a name: MIGOS (MIni GO Solver). Its search has been improved significantly (it now takes half the time to solve 5x5). We further solved all other opening moves on the empty board, which is much harder. To get an impression of the difficulty of non-center openings take a look at these games: